Method and System for 3D Reconstruction of X-ray CT Volume and Segmentation Mask from a Few X-ray Radiographs

ABSTRACT

A method and apparatus for automated reconstruction of a 3D computed tomography (CT) volume from a small number of X-ray images is disclosed. A sparse 3D volume is generated from a small number of x-ray images using a tomographic reconstruction algorithm. A final reconstructed 3D CT volume is generated from the sparse 3D volume using a trained deep neural network. A 3D segmentation mask can also be generated from the sparse 3D volume using the trained deep neural network.

BACKGROUND OF THE INVENTION

The present invention relates to automated reconstruction of a 3Dcomputed tomography (CT) volume from 2D X-ray radiographs, and moreparticularly, to automated reconstruction of a 3D CT volume and a 3Dsegmentation mask from a small number of X-ray radiographs.

X-ray computed tomography (CT) is widely used for obtaining images ofdifferent parts of the body which are more detailed than standardX-rays. In computed tomography, many X-ray images are taken from variousangles. All of these X-ray images are then processed using a tomographicreconstruction algorithm to generate the 3D CT volume data, which canthen be view as images in the axial, coronal, sagittal planes.

CT is regarded as a moderate to high radiation diagnostic technique.Moreover, acquiring a CT scan is more time consuming and expensivecompared to acquiring a standard X-ray scan. Therefore, in order todecrease patients' exposure to radiation and reduce time and cost, itwould be highly desirable to be able to reconstruct volumetric CT datausing just a few X-ray images. While such a reconstructed CT volume maynot replace an actual CT volume for all purposes, it could be used forvarious purposes, such as for the purpose of segmenting anatomicalstructures.

BRIEF SUMMARY OF THE INVENTION

The present invention provides a method and system for automatedcomputer-based reconstruction of 3D computed tomography (CT) volumesfrom a small number of X-ray radiographs. Embodiments of the presentinvention also automatically generate a 3D segmentation mask (or a 3Dsurface model) of an anatomical structure from the small number of X-rayradiographs.

In one embodiment of the present invention, a sparse 3D volume isgenerated from one or more X-ray images of a patient. A finalreconstructed 3D CT volume is generated from the sparse 3D volume usinga trained deep neural network. A 3D segmentation mask of a target objectcan be generated from the sparse 3D volume using the trained deep neuralnetwork.

These and other advantages of the invention will be apparent to those ofordinary skill in the art by reference to the following detaileddescription and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a method for automated reconstruction of a 3Dcomputed tomography (CT) volume and generation of a 3D segmentation maskfrom 2D X-ray images according to an embodiment of the presentinvention;

FIG. 2 illustrates a generative adversarial network for generating afully reconstructed 3D CT volume from an input sparse 3D volumeaccording to an embodiment of the present invention;

FIG. 3 illustrates a conditional-generative adversarial network forgenerating a fully reconstructed 3D CT volume from an input sparse 3Dvolume according to an embodiment of the present invention;

FIG. 4 illustrates a conditional-generative adversarial network coupledwith a voxel-wise cost function according to an embodiment of thepresent invention;

FIG. 5 illustrates an overview of the method of FIG. 1 and exemplaryresults of the method of FIG. 1; and

FIG. 6 is a high-level block diagram of a computer capable ofimplementing the present invention.

DETAILED DESCRIPTION

The present invention relates to a method and system for automatedcomputer-based reconstruction of 3D computed tomography (CT) volumes andgeneration of 3D segmentation masks from a small number of X-rayradiographs. Embodiments of the present invention are described hereinto give a visual understanding of the method for automatedreconstruction of 3D CT volumes and generation of 3D segmentation masks.A digital image is often composed of digital representations of one ormore objects (or shapes). The digital representation of an object isoften described herein in terms of identifying and manipulating theobjects. Such manipulations are virtual manipulations accomplished inthe memory or other circuitry/hardware of a computer system.Accordingly, is to be understood that embodiments of the presentinvention may be performed within a computer system using data storedwithin the computer system.

Embodiments of the present invention provide automated computer-basedreconstruction of a 3D CT volume from a few 2D X-ray images.Accordingly, embodiments of the present invention provide automatedreconstruction of 3D CT volumes with decreased patient exposure toradiation and reduced time and cost as compared to existingcomputer-based CT reconstruction techniques. Embodiments of the presentinvention also address the problem of automated generation of asegmentation mask (or 3D surface model) of anatomical structures of apatient. Such patient-specific models of anatomical structures are oftenused by surgeons during pre-operative surgery planning and also forimage-based guidance during surgery. Existing approaches to constructing3D surface models typically first use medical imaging techniques such asCT or magnetic resonance imaging (MRI), and then use segmentationalgorithms (either manual or automatic). However, because of excessivetime, cost, and/or radiation involved in CT and MRI, alternativeapproaches using only 2D X-ray radiographs have been proposed. Most ofthese approached use statistical shape models (SSMs). For example, inZheng at al., “3D Reconstructions of a Patient-Specific Surface Model ofthe Proximal Femur from Calibrated X-ray Radiographs: A ValidationStudy,” Medical Physics, Vol. 36, No. 4, 2009, pp. 1155-1166, iterativenon-rigid registration of features extracted from an SSM to thoseinteractively identified from the radiographs is performed. In Zheng etal., “Scaled, Patient-Specific 3D Vertebral Model Reconstruction Basedon 2D Lateral Fluoroscopy,” International Journal of Computer AssistedRadiology and Surgery, Vol. 6, No. 3, 2011, pp. 351-356, asemi-automatic method is proposed in which the user uses a segmentationtool to extract image contours. However, if the samples aresignificantly different, the method requires multiple SSMs. First the2D/3D reconstruction problem is converted into a 3D/3D problem bycomputing the corresponding 3D point pairs, and then solved using athree stage iterative method. In Baka et al., “2D-3D ShapeReconstruction of the Distal Femur from Stereo X-ray Imaging UsingStatistical Shape Models,” Medical Image Analysis, Vol. 15, No. 6, 2011,pp. 840-850, an SSM-based method is proposed for pose estimation andshape reconstruction from two or more X-ray images involving manualinitialization of the mean shape. In Schumann et al., “An IntegratedSystem for 3D Hip Joint Reconstructions from 2D X-rays: A PreliminaryValidation Study,” Annals of Biomedical Engineering, Vol. 41, No. 10,2013, pp. 2077-2087, the idea of using a motion calibration phantom toestablish the correspondences between models is introduced. Registrationof two different SSMs is performed—one from CT segmented surface modelsand the other being a hemi-pelvis SSM. The contours are extractedsemi-automatically. In, Yu et al., “Fully Automatic Reconstruction ofPersonalized 3D Volumes of the Proximal Femur from 2D X-ray Images,”International Journal of Computer Assisted Radiology, Vol. 11, No. 9,2016, pp. 1673-1685, a fully automatic reconstruction method is proposedthat uses a control point-based 2D-3D registration approach. This is atwo-stage approach involving scaled-rigid registration and regularizeddeformable B-spline registration. A uniform 3D grid of points is placedon the 3D template and the registration transformation is calculatedbased on the transformations undergone by each point in the grid.

Embodiments of the present invention provide a fully automatic methodthat generates a 3D CT volume and a segmentation mask of an anatomicalobject given 2D X-ray images of the anatomical object. Embodiments ofthe present invention can perform the automatic reconstruction of the 3DCT volume and generation of the 3D segmentation mask from only a few 2DX-ray images. This is a very ill-posed problem, in the sense that one ortwo 2D X-ray images typically do not contain enough information that isrequired to generate the complete 3D volume. Accordingly, in order totackle this problem, embodiments of the present invention cannot affordto not use any of the information available in the X-ray images. Inexisting techniques for computing 3D CT data, a large number of X-rayimages (depending on the body part this number is typically anywherefrom 100-750) are taken from various directions around the object. Allof these 2D X-ray images are then “stitched” together by a tomographicreconstruction algorithm to produce the 3D CT volume data. In theproblem addressed by embodiments of the present invention, instead ofhundreds of X-ray images, very few X-ray images are available (e.g.,less than four). Instead of using each these X-rays separately,embodiments of the present invention combine all of the available X-rayimages using a tomographic reconstruction algorithm, such as filteredback projection (FBP), to obtain a sparse 3D CT volume which has all ofthe information contained in the input 2D X-ray images and alsoadditional information of how the 2D X-ray images relate to one another.Once the sparse 3D CT volume is generated, it is passed through atrained deep neural network, such as a Conditional-GenerativeAdversarial Network, to generate the final reconstructed 3D CT volumealong with the 3D segmentation mask.

FIG. 1 illustrates a method for automated reconstruction of a 3D CTvolume and generation of a 3D segmentation mask from 2D X-ray imagesaccording to an embodiment of the present invention. The method of FIG.1 transforms 2D X-ray images of a patient's anatomy to generate areconstructed 3D CT volume and a 3D segmentation mask of a targetobject. The method of FIG. 1 requires only a small number of 2D X-rayimages (radiographs) to perform the reconstruction of the 3D CT volumeand the generation of the 3D segmentation mask. In particular, themethod of FIG. 1 can be performed using a few as two 2D X-ray images ofthe patient.

Referring to FIG. 1, at step 102, two or more 2D X-ray images arereceived. The 2D X-ray images, also referred to as radiographs, areX-ray images of a target anatomical structure of a patient obtained withan X-ray scanner at different projection angles. The 2D X-ray images canbe obtained using an X-ray scanner device, such as a stand-alone X-rayscanner, a CT scanner, or a C-arm CT scanner. The 2D X-ray images can bereceived directly from the X-ray scanner device or can be received byloading previously stored X-ray images of the patient from a memory orstorage of a computer system or receiving the X-ray images via anelectronic transmission from a remote computer system. According to anadvantageous aspect of the present invention, the method of FIG. 1 canbe performed with only a few (e.g., less than or equal to four) X-rayimages, but the present invention is not limited thereto. At least twoX-ray images are received. In an exemplary implementation, only twoX-ray images (e.g., first and second X-ray images) may be received, butthe present invention is not limited thereto.

At step 104, a sparse 3D volume is generated from the 2D X-ray images.In particular, the two or more 2D X-ray images are combined to using atomographic reconstruction algorithm, such as filtered back-projection(FBP), to generate a sparse 3D volume which has all of the informationcontained in the input 2D X-ray images and also the additionalinformation of how the input 2D X-ray images relate to each other. Thisadditional information comes from the physical principles involved inthe CT data computation by tomographic reconstruction and from the poseinformation of each of the 2D X-ray images. In some embodiments, such aswhen the X-ray images are generated using a CT scanner or C-arm CTscanner, the pose information for each 2D X-ray image is provided by theimage acquisition device and is therefore readily available for thetomographic reconstruction algorithm. In other embodiments in which thepose information is not available from the image acquisition device, therelative poses of the 2D X-ray images can be estimated. In an exemplaryembodiment, this pose estimation can be performed using a separatetrained deep neural network that is trained to take the 2D X-ray imagesas inputs and output the pose parameters. In an exemplaryimplementation, FBP can be used to generate the sparse 3D volume fromthe two or more 2D X-ray images. FBP is a well known tomographicreconstruction algorithm. However, the present invention is not limitedto filtered back-projection, and other tomographic reconstructionalgorithms can be used as well.

At step 106, a final reconstructed 3D CT volume and a 3D segmentationmask of a target object is generated from the sparse 3D volume using atrained deep neural network. Once the sparse 3D volume is generated (instep 104), the sparse 3D volume is input to and passed through a traineddeep neural network to generate the final reconstructed 3D CT volumealong with the 3D segmentation mask. The final reconstructed CT volumeis a non-sparse CT volume that will appear as if it was reconstructedfrom a full set of X-ray projection images. The 3D segmentation mask isa 3D mask showing the voxels in the final reconstructed CT volume thatare within a boundary of a target object, such as a organ, vessel, bonestructure, or other anatomical structure.

In an advantageous embodiment, the deep neural network is a deepimage-to-image network (DI2IN) and the network architecture has anencoder and decoder. For example, the DI2IN can have a deepconvolutional encoder-decoder network architecture. The encoder has aseries of layers that code the sparse 3D input information into a codewhose size is substantially less than the size of the input sparse 3Dvolume. The decoder has a series of layers that will then decode thecode into the outputs of the final reconstructed 3D volume and the 3Dsegmentation mask. All the intermediate information generated in theencoder is shared with the decoder, so that no information is lost inthe encoding process. In one exemplary implementation, the networkarchitecture can include a single decoder with multiple outputs tooutput the final reconstructed 3D CT volume and the 3D segmentationmask. In another exemplary implementation, the network architecture caninclude a single encoder and two decoders, one trained to output thefinal reconstructed 3D volume and the other trained to output the 3Dsegmentation mask. An objective function based on the distance betweenthe generated output of the deep neural network and the real groundtruth reconstructed CT volumes and 3D segmentation masks in trainingdata is used to train the deep neural network to learn the weights forthe layers of the encoder and the decoder. In an advantageousembodiment, the deep neural network can be a generative adversarialnetwork or a conditional-generative adversarial network. In this case, adiscriminator network is used together with the DI2IN during training.The discriminator network judges the output of the DI2IN and decideswhether the output looks close enough to the real ground truth trainingdata. The advantage of the discriminator is that it adds an additionalconstraint to the DI2IN during training which helps the output of theDI2IN (i.e., the final reconstructed 3D CT volume and the 3Dsegmentation mask) look as close to the real ground truth data aspossible.

In an exemplary embodiment, the deep neural network is trained as agenerative adversarial network. FIG. 2 illustrates a generativeadversarial network for generating a fully reconstructed 3D CT volumefrom an input sparse 3D volume according to an embodiment of the presentinvention. As shown in FIG. 2, a sparse 3D volume I 202 is input to agenerator G 200. The generator G 200 is a deep neural network, such as aDI2IN implemented using a convolutional encoder-decoder architecture,that generates a synthesized fully reconstructed 3D CT volume J′204. Thesynthesized fully reconstructed 3D CT volume J′ 204 and a ground truthfully reconstructed 3D CT volume J 206 are input to a discriminator D210. The discriminator D 210 is another deep neural network thatdistinguishes between the synthesized volume J′ 204 and the real volumeJ 206. During training, the generator G 200 and the discriminator D 210together play the following minimax game:

min_(G)max_(D) E _(J˜p(J))[log(D(J))]+E _(I˜p(I))[log(1−D(J′=G(I))].  (1)

The networks are trained end-to-end by iteratively adjusting theparameters (weights) of the discriminator D 210 and the generator G 200to optimize Equation (1). In Equation (1), the first term is a costrelated to the real sample J 206 and the second term is a cost relatedto the synthesized sample J′ 204. The discriminator D 210 maximizes thefunction (i.e., trying its best to distinguish between the real andsynthesized samples) and the generator G 200 minimizes the function(i.e., synthesize real looking samples to fool the discriminator). Thegenerator G 200 and the discriminator D 210 evolve dynamically in thesense of learning better network parameters until they reachequilibrium, that is, the synthesized volume J′ 204 becomes as close aspossible from being indistinguishable from the real volume J 206 throughthe eyes of the discriminator D 210. The trained generator G 200 (i.e.,DI2IN) is then stored, for example, in a memory or storage of a computersystem and used alone for inference (in step 106) in order to generate asynthesized fully reconstructed CT volume from an input sparse 3Dvolume.

It is to be understood that although FIG. 2 is described herein for asynthesized output image J′ of a fully reconstructed CT volume, FIG. 2can be similarly applied to a target output image J′ of a 3Dsegmentation mask. In a possible implementation in which the generator Ggenerates both a synthesized fully reconstructed 3D CT volume and a 3Dsegmentation mask, the generative adversarial network shown in FIG. 2can be extended to have two discriminators, one which distinguishesbetween synthesized and real fully reconstructed 3D CT volumes andanother which distinguishes between synthesized and real (ground-truth)3D segmentation masks. In this case, the function in Equation (1) can beextended to include error terms for both discriminators and the minimaxgame used for training can be played together by all three networks.

In another possible embodiment, the deep neural network can be trainedas a conditional-generative adversarial network. In aconditional-generative adversarial network, the discriminator isconditioned on the input image I. FIG. 3 illustrates aconditional-generative adversarial network for generating a fullyreconstructed 3D CT volume from an input sparse 3D volume according toan embodiment of the present invention. As shown in FIG. 3, a sparse 3Dvolume I is input to a generator G_(α) 300. The generator G_(α) 300 is adeep neural network, such as a DI2IN, that generates a synthesized fullyreconstructed 3D CT volume I′ from the input sparse 3D volume I. Theinput sparse 3D volume I, the synthesized fully reconstructed 3D CTvolume J′, and a real fully reconstructed 3D CT volume J are input to adiscriminator D_(β) 310. The discriminator D_(β) 310 is another deepneural network that distinguishes between the synthesized volume I′ andthe real volume J. During training, the generator G_(α) 300 and thediscriminator D_(β) 310 together play the following minimax game,conditioned on the input sparse 3D volume I:

min_(α)max_(β) E _(I,J˜p(I,J))[log(D_(β)(J|I))]+E _(I,J˜p(I,J))[log(1−D_(β)(J′=G _(α() i)|I))],   (2)

where α and β are the parameters (weights) of the generator G_(α) 300and the discriminator D_(β), respectively. The networks are trainedend-to-end by iteratively adjusting the parameters (weights) α and β tooptimize Equation (2). In Equation (2), the first term is a cost relatedto the real sample J and the second term is a cost related to thesynthesized sample J′. The generator G_(α) 300 and the discriminatorD_(β) 310 evolve dynamically in the sense of learning better networkparameters until they reach equilibrium, that is, the synthesized volumeJ′=G_(α)(I) becomes indistinguishable from the real volume J through theeyes of the discriminator N 310. Under such circumstances, the generatorG_(α) 300 actually generates the real fully reconstructed 3D CT volumefor the input sparse 3D volume I. The trained generator G_(α) 300 (i.e.,DI2IN) is then stored, for example, in a memory or storage of a computersystem and used alone for inference (in step 106) in order to generate asynthesized fully reconstructed CT volume from an input sparse 3Dvolume.

It is to be understood that although FIG. 3 is described herein for asynthesized output image J′ of a fully reconstructed CT volume, FIG. 3can be similarly applied to a target output image J′ of a 3Dsegmentation mask. In a possible implementation in which the generator Ggenerates both a synthesized fully reconstructed 3D CT volume and a 3Dsegmentation mask, the conditional-generative adversarial network shownin FIG. 3 can be extended to have two discriminators, one whichdistinguishes between synthesized and real fully reconstructed 3D CTvolumes, conditioned on the input sparse 3D volume, and another whichdistinguishes between synthesized and real (ground-truth) 3Dsegmentation masks, conditioned on the input sparse 3D volume. In thiscase, the function in Equation (2) can be extended to include errorterms for both discriminators and the minimax game used for training canbe played together by all three networks.

In an advantageous embodiment of the present invention, the training canintegrate a voxel-wise cost function with the conditional-generativeadversarial network framework. FIG. 4 illustrates aconditional-generative adversarial network coupled with a voxel-wisecost function according to an embodiment of the present invention. Asshown in FIG. 4, a sparse 3D volume I is input to a generator G_(α) 400.The generator G_(α) 400 is a deep neural network, such as a DI2IN, thatgenerates a synthesized fully reconstructed 3D CT volume I′ from theinput sparse 3D volume I. The input sparse 3D volume I, the synthesizedfully reconstructed 3D CT volume J′, and a real (ground truth) fullyreconstructed 3D CT volume J are input to a discriminator D_(β) 410. Thediscriminator D_(β) 410 is another deep neural network thatdistinguishes between the synthesized volume J′ and the real volume J.In addition to being input to the discriminator D_(β) 410, thesynthesized fully reconstructed 3D CT volume J′ is also input to a costfunction C_(γ) 420 having parameters y. The cost function C_(γ) 420compares the synthesized fully reconstructed 3D CT volume J′ for a giveninput sparse 3D volume I with the ground-truth fully reconstructed 3D CTvolume J for that input sparse 3D volume I. In an exemplaryimplementation, the cost function C_(γ) 420 computes a voxel-wiseerror/distance between the synthesize volume I′ and the ground truthvolume J. For example, the cost function C_(γ) 420 may be implementedusing a regressive or logistic function.

During training, the parameters a of the generator G_(α) 300 and theparameters β of the discriminator D_(β) 310 are learned to optimize thefollowing minimax game, conditioned on the input sparse 3D volume I:

min_(α)max_(β) E _(I,J˜p(i,J)) [C _(γ)(J,J′=G _(α)(I)|I)]+E_(I,J˜p(I,j))[log(D _(β)(j|I)]+E _(I,J·p(I,J))[log(1−D _(β)(J′=G_(α)(I)|I)].   (3)

In Equation (3), the first term is a cost computed by the cost functionC_(γ) 420, the second term cost related to the classification of thereal sample J by the discriminator D_(β) 410, and the third term is acost related to the classification of the synthesized sample I′ by thediscriminator D_(β) 410. Given a set of N training pairs {(I_(n),J_(n))}, the task in training is to learn parameters α and β that yieldthe solution to the following cost function in which the expectationvalue is replaced by the sample average over the set of trainingsamples:

$\begin{matrix}{\min_{\alpha}{\max_{\beta}{\frac{1}{N}{\sum\limits_{n = 1}^{N}{\left\lbrack {{C_{\gamma}\left( {J_{n},{J_{n}^{\prime} = \left. {G_{\alpha}\left( I_{n} \right)} \middle| I_{n} \right.}} \right)} + {\log \left( {D_{\beta}\left( J_{n} \middle| I_{n} \right)} \right)} + {\log \left( {1 - {D_{\beta}\left( {J_{n}^{\prime} = \left. {G_{\alpha}\left( I_{n} \right)} \middle| I_{n} \right.} \right)}} \right)}} \right\rbrack.}}}}} & (4)\end{matrix}$

In the embodiment described herein using the cost function in Equation(4), the parameters y of the cost function C_(γ) 420 are preset and notadjusted in the training. In another possible implementation, dependingof the formulation of the cost function C_(γ) 420, the parameters γ canalso be adjusted together with the parameters α and β during training tooptimize the cost function.

The parameters α and β that optimize the cost function in Equation (4)are learned by iteratively alternating the following two steps until theparameters α and β converge (or until a preset maximum number oftraining iterations is reached):

-   -   Step 1—With the parameters a of the generator G_(α) 400 fixed,        solve the following maximization task for the parameters β of        the discriminator D_(β) 410:

$\max_{\beta}{\frac{1}{N}{\sum\limits_{n = 1}^{N}{\left\lbrack {{\log \left( {D_{\beta}\left( J_{n} \middle| I_{n} \right)} \right)} + {\log \left( {1 - {D_{\beta}\left( {J_{n}^{\prime} = \left. {G_{\alpha}\left( I_{n} \right)} \middle| I_{n} \right.} \right)}} \right)}} \right\rbrack.}}}$

-   -   In the advantageous implementation, in which a deep neural        network is used to model the discriminator D_(β) 410, a        backpropagation step can be implemented based on a minibatch of        training pairs in order to perform this maximization task.    -   Step 2—With the β of the discriminator D_(β) 410 fixed, solve        the following minimization task for the parameters α of the        generator G_(α) 400:

$\min_{\alpha}{\frac{1}{N}{\sum\limits_{n = 1}^{N}{\left\lbrack {{C_{\gamma}\left( {J_{n},{J_{n}^{\prime} = \left. {G_{\alpha}\left( I_{n} \right)} \middle| I_{n} \right.}} \right)} + {\log \left( {1 - {D_{\beta}\left( {J_{n}^{\prime} = \left. {G_{\alpha}\left( I_{n} \right)} \middle| I_{n} \right.} \right)}} \right)}} \right\rbrack.}}}$

It is practically found that, rather than training G_(α) 400 to minimizelog(1−D_(β)(J′)), training G_(α) 400 to maximize log (D_(β)(J′)) leadsto better gradient signals early in learning, even though both objectivefunctions yield the same fixed point. Accordingly, in an advantageousimplementation, the parameters α of the generator G_(α) 400 can belearned in step 2 using the following minimization problem:

$\min_{\alpha}{\frac{1}{N}{\sum\limits_{n = 1}^{N}{\left\lbrack {{C_{\gamma}\left( {J_{n},{J_{n}^{\prime} = \left. {G_{\alpha}\left( I_{n} \right)} \middle| I_{n} \right.}} \right)} - {\log \left( {D_{\beta}\left( {J_{n}^{\prime} = \left. {G_{\alpha}\left( I_{n} \right)} \middle| I_{n} \right.} \right)} \right)}} \right\rbrack.}}}$

-   -   In the advantageous implementation, in which a deep neural        network (e.g. DI2IN) is used to model the discriminator D_(β)        410, a backpropagation step can be implemented based on a        minibatch of training pairs in order to perform this        minimization task.

Once the training is complete, the trained generator G 400 (i.e., DI2IN)is then stored, for example, in a memory or storage of a computer systemand used alone for inference (in step 106) in order to generate asynthesized fully reconstructed CT volume from an input sparse 3Dvolume. It is to be understood that although FIG. 4 is described hereinfor a synthesized output image J′ of a fully reconstructed CT volume,FIG. 4 can be similarly applied to a target output image J′ of a 3Dsegmentation mask. In a possible implementation in which the generator Ggenerates both a synthesized fully reconstructed 3D CT volume and a 3Dsegmentation mask, the conditional-generative adversarial network shownin FIG. 4 can be extended to have two discriminators, one whichdistinguishes between synthesized and real fully reconstructed 3D CTvolumes and another which distinguishes between synthesized and real(ground-truth) 3D segmentation masks, and two voxel-wise cost functions,one that compares synthesized and ground-truth fully reconstructed 3D CTvolumes and another that compares synthesized and ground-truth 3Dsegmentation masks. In this case, the functions in Equations (3) and (4)can be extended to include error terms for both discriminators and bothcost functions, and the training to learn the network parameters can beiteratively alternate between all three networks.

Returning to FIG. 1, at step 108, the final reconstructed 3D CT imageand the 3D segmentation mask of the target object are output. The finalreconstructed 3D CT image and the 3D segmentation mask of the targetobject can be output by displaying the final reconstructed 3D CT imageand the 3D segmentation mask of the target object on a display device ofa computer system. For example, the final reconstructed 3D CT imageand/or the 3D segmentation mask of the target object can be displayed ona displayed device as a 3D visualization or by displaying various 2Dslices extracted from the final reconstructed 3D CT image and/or the 3Dsegmentation mask of the target object.

FIG. 5 illustrates an overview of the method of FIG. 1 and exemplaryresults of the method of FIG. 1. As shown in FIG. 5, a first 2D X-rayview 502 and a second 2D x-ray view 504 are obtained for a patient. Atomographic reconstruction algorithm 506, such as FBP, is used togenerate a sparse 3D volume 508 from the first and second X-ray views502 and 504. The sparse 3D volume 508 is input to a trained deep neuralnetwork 510, and the trained deep neural network 510 generates a finalreconstructed 3D CT volume 512 and a 3D segmentation mask 514 of atarget object. In the exemplary results shown in FIG. 5, the targetobject is the bone structures in the knee. Accordingly, thereconstructed 3D segmentation mask 514 is a reconstructed 3D bone maskof the knee.

In the embodiment of FIG. 1, a final reconstructed 3D CT image and a 3Dsegmentation mask are generated from two or more 2D x-ray images of apatient. In an alternative embodiment, a final reconstructed 3D CT imageand/or a 3D segmentation mask can be similarly generated using a single2D x-ray image. In this case, a second x-ray image at a different poseis first estimated based on the single x-ray image using a trained deepimage-to-image neural network. Then, the tomographic reconstructionalgorithm is used to generate a sparse 3D volume from the original x-rayimage of the patient and the estimated second x-ray image. This sparse3D volume is then input to a trained deep neural network, whichgenerates the final reconstructed 3D CT volume and the 3D segmentationmask based on the sparse 3D volume as described above in step 106 ofFIG. 1.

The method of FIG. 1 described above generates a final reconstructed 3DCT volume from a small number of x-ray images. This method may besimilarly applied to reconstruct 3D volumes of medical imaging otherthan CT. Depending on the image modality to be reconstructed, a suitablesparse reconstruction can first be generates based on the physicalprinciples involved in that particular imaging modality, and then atrained deep neural network can be used to generate the targetreconstructed 3D outputs from the sparse reconstruction.

The above-described method for automated reconstruction of a 3D CTvolume and generation of a 3D segmentation mask from 2D X-ray images maybe implemented on a computer using well-known computer processors,memory units, storage devices, computer software, and other components.A high-level block diagram of such a computer is illustrated in FIG. 6.Computer 602 contains a processor 604, which controls the overalloperation of the computer 602 by executing computer program instructionswhich define such operation. The computer program instructions may bestored in a storage device 612 (e.g., magnetic disk) and loaded intomemory 610 when execution of the computer program instructions isdesired. Thus, the steps of the method of FIG. 1 may be defined by thecomputer program instructions stored in the memory 610 and/or storage612 and controlled by the processor 604 executing the computer programinstructions. An image acquisition device 620, such as a CT scanner,C-arm CT scanner, or X-ray scanner, can be connected to the computer 602to input image data to the computer 602. It is possible to implement theimage acquisition device 620 and the computer 602 as one device. It isalso possible that the image acquisition device 620 and the computer 602communicate wirelessly through a network. In a possible embodiment, thecomputer 602 can be located remotely with respect to the imageacquisition device 620 and the method steps described herein can beperformed as part of a server or cloud based service. In this case, themethod steps may be performed on a single computer or distributedbetween multiple networked computers. The computer 602 also includes oneor more network interfaces 606 for communicating with other devices viaa network. The computer 602 also includes other input/output devices 608that enable user interaction with the computer 602 (e.g., display,keyboard, mouse, speakers, buttons, etc.). Such input/output devices 608may be used in conjunction with a set of computer programs as anannotation tool to annotate images/volumes received from the imageacquisition device 620. One skilled in the art will recognize that animplementation of an actual computer could contain other components aswell, and that FIG. 6 is a high level representation of some of thecomponents of such a computer for illustrative purposes.

The foregoing Detailed Description is to be understood as being in everyrespect illustrative and exemplary, but not restrictive, and the scopeof the invention disclosed herein is not to be determined from theDetailed Description, but rather from the claims as interpretedaccording to the full breadth permitted by the patent laws. It is to beunderstood that the embodiments shown and described herein are onlyillustrative of the principles of the present invention and that variousmodifications may be implemented by those skilled in the art withoutdeparting from the scope and spirit of the invention. Those skilled inthe art could implement various other feature combinations withoutdeparting from the scope and spirit of the invention.

1. A method for automated reconstruction of a 3D computed tomography(CT) volume one or more X-ray images, comprising: generating a sparse 3Dvolume from one or more X-ray images of a patient; and generating afinal reconstructed 3D CT volume from the sparse 3D volume using atrained deep neural network.
 2. The method of claim 1, wherein the oneor more X-ray images of the patient comprise a first x-ray image and asecond x-ray image, and generating the sparse 3D volume from the one ormore X-ray images of the patient comprises: generating the sparse 3Dvolume from the first X-ray image and the second X-ray image using atomographic reconstruction algorithm.
 3. The method of claim 2, whereinthe one or more x-ray images of the patient comprise only the first andsecond x-ray images, and generating the sparse 3D volume from the firstX-ray image and the second X-ray image using a tomographicreconstruction algorithm comprises: generating the sparse 3D volume fromthe first X-ray image and the second X-ray image without any additionalx-ray images using a tomographic reconstruction algorithm.
 4. The methodof claim 1, further comprising: generating a 3D segmentation mask of atarget object from the sparse 3D volume using the trained deep neuralnetwork.
 5. The method of claim 4, wherein the trained deep neuralnetwork is a multi-output deep image-to-image network having encoderlayers that code the sparse 3D volume into a code whose size is smallerthan the spare 3D volume and decoder layers that decode the code intothe final reconstructed 3D volume and the and the 3D segmentation maskof the target object.
 6. The method of claim 1, wherein the trained deepneural network is a deep image-to-image network that is trained in agenerative adversarial network together with a discriminator network fordistinguishing between synthesized reconstructed 3D CT volumes generatedby the deep image-to-image network from input sparse 3D volume trainingsamples and real reconstructed 3D CT volume training samples.
 7. Themethod of claim 1, wherein the trained deep neural network is a deepimage-to-image network that is trained in a conditional-generativeadversarial network together with a discriminator network fordistinguishing between synthesized reconstructed 3D CT volumes generatedby the deep image-to-image network from input sparse 3D volume trainingsamples and real reconstructed 3D CT volume training samples,conditioned on the input sparse 3D volume training samples.
 8. Themethod of claim 7, wherein the conditional-generative adversarialnetwork is integrated with a voxel-wise cost function that computes avoxel-wise error between the synthesized reconstructed 3D CT volumesgenerated by the deep image-to-image network from input sparse 3D volumetraining samples and corresponding ground-truth reconstructed 3D CTvolume training samples, and the deep image-to-image network and thediscriminator network are trained together to optimize, over a pluralityof training samples, a minimax objective function that includes a firstterm that calculates an error using the voxel-wise cost function, asecond term that calculates an error of the discriminator networkclassifying the real reconstructed 3D CT training samples, and a thirdterm that calculates and error of the discriminator network classifyingthe synthesized reconstructed 3D CT volumes generated by the deepimage-to-image network.
 9. An apparatus for automated reconstruction ofa 3D computed tomography (CT) volume one or more X-ray images,comprising: means for generating a sparse 3D volume from one or moreX-ray images of a patient; and means for generating a finalreconstructed 3D CT volume from the sparse 3D volume using a traineddeep neural network.
 10. The apparatus of claim 9, further comprising:means for generating a 3D segmentation mask of a target object from thesparse 3D volume using the trained deep neural network.
 11. Theapparatus of claim 9, wherein the trained deep neural network is a deepimage-to-image network that is trained in a generative adversarialnetwork together with a discriminator network for distinguishing betweensynthesized reconstructed 3D CT volumes generated by the deepimage-to-image network from input sparse 3D volume training samples andreal reconstructed 3D CT volume training samples.
 12. The apparatus ofclaim 9, wherein the trained deep neural network is a deepimage-to-image network that is trained in a conditional-generativeadversarial network together with a discriminator network fordistinguishing between synthesized reconstructed 3D CT volumes generatedby the deep image-to-image network from input sparse 3D volume trainingsamples and real reconstructed 3D CT volume training samples,conditioned on the input sparse 3D volume training samples.
 13. Theapparatus of claim 12, wherein the conditional-generative adversarialnetwork is integrated with a voxel-wise cost function that computes avoxel-wise error between the synthesized reconstructed 3D CT volumesgenerated by the deep image-to-image network from input sparse 3D volumetraining samples and corresponding ground-truth reconstructed 3D CTvolume training samples, and the deep image-to-image network and thediscriminator network are trained together to optimize, over a pluralityof training samples, a minimax objective function that includes a firstterm that calculates an error using the voxel-wise cost function, asecond term that calculates an error of the discriminator networkclassifying the real reconstructed 3D CT training samples, and a thirdterm that calculates and error of the discriminator network classifyingthe synthesized reconstructed 3D CT volumes generated by the deepimage-to-image network.
 14. A non-transitory computer-readable mediumstoring computer program instructions for automated reconstruction of a3D computed tomography (CT) volume one or more X-ray images, thecomputer program instructions when executed by a processor cause theprocessor to perform operations comprising: generating a sparse 3Dvolume from one or more X-ray images of a patient; and generating afinal reconstructed 3D CT volume from the sparse 3D volume using atrained deep neural network.
 15. The non-transitory computer-readablemedium of claim 14, wherein the one or more X-ray images of the patientcomprise a first x-ray image and a second x-ray image, and generatingthe sparse 3D volume from the one or more X-ray images of the patientcomprises: generating the sparse 3D volume from the first X-ray imageand the second X-ray image using a tomographic reconstruction algorithm.16. The non-transitory computer-readable medium of claim 14, wherein theoperations further comprise: generating a 3D segmentation mask of atarget object from the sparse 3D volume using the trained deep neuralnetwork.
 17. The non-transitory computer-readable medium of claim 16,wherein the trained deep neural network is a multi-output deepimage-to-image network having encoder layers that code the sparse 3Dvolume into a code whose size is smaller than the spare 3D volume anddecoder layers that decode the code into the final reconstructed 3Dvolume and the and the 3D segmentation mask of the target object. 18.The non-transitory computer-readable medium of claim 14, wherein thetrained deep neural network is a deep image-to-image network that istrained in a generative adversarial network together with adiscriminator network for distinguishing between synthesizedreconstructed 3D CT volumes generated by the deep image-to-image networkfrom input sparse 3D volume training samples and real reconstructed 3DCT volume training samples.
 19. The non-transitory computer-readablemedium of claim 14, wherein the trained deep neural network is a deepimage-to-image network that is trained in a conditional-generativeadversarial network together with a discriminator network fordistinguishing between synthesized reconstructed 3D CT volumes generatedby the deep image-to-image network from input sparse 3D volume trainingsamples and real reconstructed 3D CT volume training samples,conditioned on the input sparse 3D volume training samples.
 20. Thenon-transitory computer-readable medium of claim 19, wherein theconditional-generative adversarial network is integrated with avoxel-wise cost function that computes a voxel-wise error between thesynthesized reconstructed 3D CT volumes generated by the deepimage-to-image network from input sparse 3D volume training samples andcorresponding ground-truth reconstructed 3D CT volume training samples,and the deep image-to-image network and the discriminator network aretrained together to optimize, over a plurality of training samples, aminimax objective function that includes a first term that calculates anerror using the voxel-wise cost function, a second term that calculatesan error of the discriminator network classifying the real reconstructed3D CT training samples, and a third term that calculates and error ofthe discriminator network classifying the synthesized reconstructed 3DCT volumes generated by the deep image-to-image network.